Are there family traditions or games or particular rules that help teach children about self-restraint, self-control, etc.?
One custom we had at my house was that there were many manners to learn at the dinner table. Each violation earned the offender 1 point. At the end of dinner, the two kids with the most points washed and dried the dishes. The one with the least points got to pick which of the two they wanted (wash or dry). Things like "elbows on the table", "talking with mouth full" and "slurping" were eliminated and mom didn't have to do the dishes. Win for the parents :) From this I learned to be watchful of my manners
Rewards are a good way to motivate children towards the kinds of behavior you want. Games or traditions which build in rewards work well.
An example of this is when I was little I had the tendency to talk non-stop sometimes, which really annoyed my family on long car trips. My family told me that if I was silent and didn't say a word they would get me an ice cream at the next Dairy Queen we passed. I had a burning desire to blab, but the thought of a reeses peanut butter cup blizzard was greater and it worked. They got peace and quiet and I got an ice cream, but I also leaned to be quieter that way.